Analysis of the latent subspaces
To show that our method is capable of inferring the correct number of subspaces, and also to show how properly they are characterized, we perform a qualitative and quantitative analysis on the latent subspaces (Figure REF ). We project each latent subspace (approximated by randomly sampling 512 elements in the dataset) onto a 2-dimensional subspace, using the dimensionality reduction technique of (t-SNE) [1]}. We show which subspace encodes information about which factor by counting the number of clusters that are formed by t-SNE. At convergence, the number of clusters will correspond loosely to the number of possible values that the generative factor can assume (e.g. if the true distribution of the generative factor is discrete and 10-dimensional, we expect to count 10 clusters). We can also see that our algorithm is capable of inferring the correct number of subspaces from an overestimate, this reflects in the fact that when a factor does not encode any information it collapses to a single cluster. We accompany each latent subspace projection plot with an interpolation of pair of samples, which differ on each factor of variation on each of the subspace. These results are supported by the quantitative evidence in Table REF , where we measure the average standard deviation in each subspace on the same random sampling plotted in 2 dimensions; we show that there is a strong gap between variance in the subspaces that encode information, and those that are collapsed.
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